Abstract
I apply the notions of alethic reference introduced in previous work in the construction of several classical semantic truth theories. Furthermore, I provide proof-theoretic versions of those notions and use them to formulate axiomatic disquotational truth systems over classical logic. Some of these systems are shown to be sound, proof-theoretically strong, and compare well to the most renowned systems in the literature.
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Acknowledgements
I am deeply indebted to Volker Halbach, with whom I had countless fruitful discussions on reference and self-reference over the last six years. I would also like to particularly thank Dan Waxman for extremely helpful comments on the final drafts, Thomas Schindler, for great suggestions and encouragement, and two anonymous referees for serious improvements in clarity and exposition. I should mention as well Eduardo Barrio, Catrin Campbell-Moore, Luca Castaldo, Roy T. Cook, Benedict Eastaugh, Martin Fischer, Hannes Leitgeb, Øystein Linnebo, Carlo Nicolai, Graham Priest, Johannes Stern, Albert Visser, the Buenos Aires Logic Group, the MCMP logic community, and the Oxford logic group. Finally, I would like to thank the Alexander von Humboldt Foundation and, especially, the Deutsche Forschungsgemeinschaft (DFG) for generously funding the research projects “Reference patterns of paradox” (PI 1294/1-1) and “The Logics of Truth: Operational and Substructural Approaches” (GZ HJ 5/1-1, AOBJ 617612).
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Picollo, L. Reference and Truth. J Philos Logic 49, 439–474 (2020). https://doi.org/10.1007/s10992-019-09525-9
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DOI: https://doi.org/10.1007/s10992-019-09525-9